Answer:
The original price of the shirt was Ksh 500 and it was sold for Ksh 550.
The discount is the difference between the original price and the selling price, which is Ksh 500 - Ksh 550 = Ksh -50.
To find the percentage discount, we can use the formula:
percentage discount = (discount ÷ original price) × 100%
percentage discount = (-50 ÷ 500) × 100%
percentage discount = -10%
Therefore, the percentage discount is 10%.
Solve for w.
W
9
10
||
45
Answer:
W=26........
Step-by-step explanation:
26+9+10=45
Find the formula for the nth term of the arithmetic sequence whose first term and a common difference are given: a=1, d=5
The arithmetic sequence is solved and the nth term is aₙ = 5n - 4
Given data ,
The formula for the nth term of an arithmetic sequence is:
aₙ = aₙ1 + (n - 1)d
where a₁ is the first term, d is the common difference, and n is the term number.
In this case, a₁ = 1 and d = 5, so the formula becomes:
aₙ = 1 + (n - 1)5
Simplifying, we get:
aₙ = 5n - 4
Hence , the formula for the nth term of the arithmetic sequence with first term 1 and common difference 5 is aₙ = 5n - 4
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If p(x)=0.5(x-5)^2+14, what is the value of p(3)
Answer:
p(3) = 16
Step-by-step explanation:
to evaluate p(3) substitute x = 3 into p(x)
p(3) = 0.5(3 - 5)² + 14
= 0.5(- 2)² + 14
= 0.5(4) + 14
= 2 + 14
= 16
Prove the following?
If a subset A of natural numbers (N) satisfies the conditions 0 ∈ A and if n ∈ A, then n+1 ∈ A, then A must be equal to the set of all natural numbers (N).
We will use a proof by contradiction to demonstrate this.
Assume that there exists a subset A of natural numbers that satisfies the given conditions, but A is not equal to N.
This means there exists a natural number k that is not in A.
Let B = N - A be the set of natural numbers that are not in A.
B is non-empty because it contains at least k.
Since 0 ∈ A, but k ∉ A, there must be a smallest natural number in B. Let's denote it as b.
Now, according to the given conditions, if n ∈ A, then n+1 ∈ A.
We can apply this repeatedly to obtain n+1, (n+1)+1, (n+1)+1+1, and so on.
Considering b-1, it is a natural number that is not in B because b is the smallest natural number in B. So, b-1 ∈ A.
Using the condition that if n ∈ A, then n+1 ∈ A, we can apply it repeatedly to b-1 to get (b-1)+1, (b-1)+1+1, and so on.
This implies that b, b+1, b+2, and so on, all belong to A.
However, this contradicts the fact that b is the smallest natural number in B, and A is defined such that it includes all natural numbers greater than or equal to 0.
Therefore, our assumption that A is not equal to N is false, and we can conclude that A = N.
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How many different positive integers n are there for which n and n^2+3 are both prime numbers?
That value being n = 2
============================================================
Explanation:
The only even prime number is n = 2. This leads to n^2+3 = 2^2+3 = 7 which is also prime. So far we found one such value of n that fits the criteria.
-----------
If n is odd, then n^2 is also odd.
The quick proof goes like this: let n = 2k+1 for some integer k. This guarantees n to be odd. Then n^2 = (2k+1)^2 = 4k^2+4k+1 = 2(2k^2+2k)+1 = 2*(some integer)+1 = some odd integer.
------------
If n is prime and n isn't equal to 2, then n must be odd.
If n was even and n > 2, then it would be a multiple of 2 by definition, and would rule out it being prime. Example: n = 16 is not prime since 2 is a factor.
So n must be odd if we want to find more numbers to fit the given criteria. That makes n^2 being odd as well from the previous section's proof.
But then we use the idea that:
odd + odd = even
I'll leave the proof of this to the reader.
The sum of any two odd numbers gives an even number. An example would be 3+5 = 8.
n is prime and not 2 ---> n is odd --> n^2 is odd ---> n^2+3 = odd+odd = evenn^2+3 being even means n^2+3 cannot possibly be prime.There are no odd values of n that are prime and n^2+3 is prime.
We therefore can conclude there's only one value of n that is prime and n^2+3 is also prime. That value being n = 2.
Binomial problems Basic
The workers' union at a particular university is quite strong. About 96% of all workers employed by the university belong to the workers' union. Recently, the
workers went on strike, and now a local TV station plans to interview 5 workers (chosen at random) at the university to get their opinions on the strike. What is
the probability that exactly 4 of the workers interviewed are union members?
Round your response to at least three decimal places. (If necessary, consult a list of formulas)
0
If the workers' union at a particular university is quite strong. the probability that exactly 4 of the workers interviewed are union members is 0.1699.
What is the probability?You must count all conceivable outcomes as well as favourable outcomes in order to compute probability. The number of favourable outcomes divided by the total number of possible outcomes yields the chance that an event will occur.
Using this formula to the probability
P(X = k) = (n choose k) * [tex]p^{k}[/tex] * [tex](1-p)^{n-k}[/tex]
Where:
X = random variable
n = 5
p = 0.96
k = 4
Let plug in the formula
P(X = 4) = (5 choose 4) *[tex]0.96^{4}[/tex] *[tex](1-0.96)^{5-4}[/tex]
= 5 *[tex]0.96^{4}[/tex] * 0.04
= 0.1699
Therefore the probability is 0.1699.
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Write an expression for the calculation.
Add 3 to the product of 12 and the sum of 14 and 19.
A.
12
×
14
×
19
+
3
B.
3
+
(
12
×
14
)
+
19
C.
3
+
12
×
(
14
+
19
)
D.
3
+
(
12
×
14
+
19
)
The expression for the calculation is:
[tex]\sf 3+12\times(14+19)[/tex]
Key terms in algebraLet us focus on "product of... and the sum of..." first. Whenever you have procedures arranged in an order similar to this, always remember that the second keyword tells you to put a mathematical operation inside grouping symbols, while the first keyword tells you to keep an operation isolated on the outside. In this exercise, the product of 12 tells you that you will be distributing it amongst another individual or set inside grouping symbols, which in this case is a "set inside grouping symbols" because the sum of 14 and 19 tells you that in order to complete the produced expression, the additive expression must be placed inside grouping symbols. Now, all we have left is 3, which can be added on either side of the entire expression because according to the order of operations, in this case, multiplication is performed before addition.
Hence the expression for the calculation is
[tex]\sf 3+12\times(14+19)[/tex]
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what is the area of the figure above?
The area of the given figure is 12/25 cm²
According to the question, one grid represents 1/5 cm.
So, the dimensions of the shown rectangle are as follows:
Length of the rectangle = 4 grids = 4 × 1/5 cm = 4/5 cm
Width of the rectangle = 3 grids = 3 × 1/5 cm = 3/5 cm
As we know that the area of a rectangle is defined as the product of the length and width.
The area of the figure = Length of the rectangle × Width of the rectangle
The area of the figure = 4/5 cm × 3/5 cm
The area of the figure = 12/25 cm²
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triangular prism and its dimensions in centimeters are shown in the diagram.
What is the total surface area of the prism in square centimeters?
A. 720 cm^2
B. 600 cm^2
C. 460 cm^2
D. 520 cm^2
The total surface area of the triangular prism is equal to 520 square centimeters. (Correct choice: D)
How to determine the total surface area of a triangular prismIn this problem we find the case of a triangular prism, which has two triangular faces and three rectangular faces. We must determine the total surface area with the help of the following area formulas:
Rectangle
A = b · h
Triangle
A = 0.5 · b · h
Where:
b - Base, in centimetersh - Height, in centimetersA - Area, in square centimeters.Now we proceed to determine the total surface area of the prism:
A = 2 · 0.5 · (15 cm) · (8 cm) + (10 cm) · (8 cm) + (17 cm) · (10 cm) + (15 cm) · (10 cm)
A = 120 cm² + 80 cm² + 170 cm² + 150 cm²
A = 520 cm²
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What is the area?
Write your answer as a fraction or as a whole or mixed number.
51 ft
10
2 º/ ft
square feet
The area of the rectangle is 1632/3 square feet.
To calculate the area, we need to multiply the length and width of the given rectangle. The length is 51 feet, and the width is 10 2/3 feet, which can be expressed as an improper fraction as 32/3 feet.
Multiplying these values, we have:
Area = length × width
= 51 ft × (32/3) ft
= (51 × 32)/(3)
= 1632/3 square feet
So, the area of the rectangle is 1632/3 square feet.
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5x = 135. What is the value of x?
Answer:
Step-by-step explanation:
17
5 divided by 135
A 50.0 mL aliquot of a 1.25 M solution of glucose (C6H12O6) is added to 100.0 mL of pure water. What is the molarity of the resulting solution? A) 0.26 M B) 0.35 M C) 0.42 M D) 0.67 M E) 0.125 M
The molarity of the resulting solution is 0.42 M (rounded to two significant figures), which is option C.
To solve this problem, we can use the equation:
M₁V₁= M₂V₂
where M₁ is the initial molarity, V₁ is the initial volume, M₂ is the final molarity, and V₂ is the final volume.
We are given that the initial volume is 50.0 mL and the initial molarity is 1.25 M. We are also told that 100.0 mL of water is added to the solution, so the final volume is 50.0 mL + 100.0 mL = 150.0 mL.
Plugging these values into the equation, we get:
(1.25 M)(50.0 mL) = M2(150.0 mL)
Solving for M₂, we get:
M₂ = (1.25 M)(50.0 mL) / (150.0 mL) = 0.4167 M
Therefore, the molarity of the resulting solution is 0.42 M (rounded to two significant figures), which is option C.
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Given that events A and B are independent with P(A) = 0.26 and P(B|A) = 0.7,
determine the value of P(B), rounding to the nearest thousandth, if necessary.
The value of P(B) is 0.7.
We are given that there are two events A and B which are independent of each other. It means that they are mutually exclusive. We are also given the value of P(A) = 0.26 and [tex]P(B|A)[/tex] = 0.7. We have to determine the value of P(B).
We will use the formula of conditional probability to solve this question.
The formula for conditional probability;
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
As we know that A and B are independent events, Therefore
P( A [tex]\cap[/tex] B ) = P(A). P(B)
Substituting the value of [tex]P(A \cap B)[/tex] in the formula of conditional probability,
Therefore,
[tex]P(B|A)[/tex] = [tex]\frac{P(A) P(B)}{P(A)}[/tex]
We are given that [tex]P(B|A)[/tex] is 0.7, we will substitute this value.
0.7 = P(B)
Therefore, the value of P(B) is 0.7 after rounding it to the nearest thousandth.
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Lauren earns $1485 per month. What is the maximum amount she
should budget for housing? show your work
The maximum amount Lauren should budget for housing is $445.50 per month.
Now, A good rule of thumb is that housing expenses should not exceed 30% of her income.
So, We get;
30% of Lauren's monthly income of $1485 would be:
= 30% x $1485
= $445.50
Therefore, the maximum amount Lauren should budget for housing is $445.50 per month.
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23. Loom bands come in packs of 100. Natalie has 7 full packs and 57 other bands.
What decimal represents the number of packs of loom bands that Natalie has?
The decimal that represents the number of packs of loom bands that Natalie has is 7.57.
We can see that Natalie has 7 full packs of loom bands, which is a total of:
7*100= 700 loom bands
In addition, she has 57 other bands, making a total of:
700+57 =757 loom bands.
Now to find the decimal that represents the number of packs Natalie has, we need to divide the total number of loom bands by 100, since there are 100 bands in each pack. Thus, we have:
757 / 100 = 7.57
Therefore, the decimal that represents the number of packs of loom bands that Natalie has is 7.57.
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a man is standing on the edge of a cruise ship for animals with his binoculars he sees a seagull at an angle of eleevatuoj of 27 degrees and his binoculars tell him that the seagull is 94 feet away he also notices a dolphin at an angle of deepens ion it 46 degrees and knows that his binoculars eyesight is 44 feet agout lenses level solve for how high the seagull is above sea level and how far the man binoculars are from the dolphin
The seagull is approximately 47.86 feet above sea level, and the man's binoculars are approximately 46.25 feet away from the dolphin.
Let's denote the height of the seagull above sea level as "h" and the distance between the man's binoculars and the dolphin as "d."
For the seagull:
We have the angle of elevation as 27 degrees and the distance from the man's binoculars as 94 feet.
Using the tangent function, we can write:
tan(27 degrees) = h / 94
Solving for h, we have:
h = 94 × tan(27 degrees)
For the dolphin:
We have the angle of depression as 46 degrees and the distance from the man's binoculars as 44 feet (lenses level).
Using the tangent function, we can write:
tan(46 degrees) = h / d
Solving for d, we have:
d = h / tan(46 degrees)
Now, let's calculate the values:
h = 94 × tan(27 degrees) ≈ 47.86 feet
d = (47.86 feet) / tan(46 degrees) ≈ 46.25 feet
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Will give brainliest
mathworldwolfram
SOHCAHTOA
sine equals opposite over hypotenuse, cosine equals adjacent over hypotenuse, and tangent equals opposite over adjacent
Quadrants
2 1
4 3
for a 1,2,√3 TRIANGLE
where a = 1 o = √3 h = 2
π = 180
tan 60 = 180/3 = π/3
tan 60 = π/3 in radians = √3/1 in degrees
tan 225 = (5*180)/4 = 5π/4 = -√2/2 in degrees
sin90 = π/2 in radians = soh = 1/2
sin150 = 5π/6 in radians = soh -√3/2
cos 90 = π/2 in radians = cah 1/2
tan 240 = 4π/3 in radians = toa = -√3/1
Place the indicated product in the proper location on the grid.
(m 3n + 8)(m 3n - 5)
The value of the product of expression is,
⇒ m⁶n² + 3m³n - 40
We have to given that;
Expression is,
⇒ (m³n + 8) (m³n - 5)
Now, We can product the expression is,
⇒ (m³n + 8) (m³n - 5)
⇒ m⁶n² - 5m³n + 8m³n - 40
⇒ m⁶n² + 3m³n - 40
Thus, The value of the product of expression is,
⇒ m⁶n² + 3m³n - 40
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Can someone help me with this please.
Find all the zeros of the polynomial p(x)=x^3+x^2+8x-60
--------------------------
Enter the zeros separated by commas. Enter exact values, not decimal approximations, using square roots as needed.
The zeros of the polynomial p(x) = x³ + x² + 8x - 60 will be (- 2 + √4 i), (- 2 - √4 i) and 3.
Given that:
Polynomial, p(x) = x³ + x² + 8x - 60
A polynomial expression is an algebraic expression with variables and coefficients. Unknown variables are what they're termed. We can use addition, subtraction, and other mathematical operations. However, a variable is not divisible.
At x = 3, then we have
p(3) = 3³ + 3² + 8(3) - 60
p(3) = 60 - 60
p(3) = 0
The one zeros are 3. Then the other two zeros are given as,
(x³ + x² + 8x - 60) / (x - 3) = 0
[(x - 3)(x² + 4x + 20)] / (x - 3) = 0
x² + 4x + 20 = 0
x = [-4 ± √(4² - 4 × 1 × 20)] / (2 × 1)
x = - 2 ± √4 i
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This proportion can be solved to find the unknown length, x
, in the smaller triangle.
128=x2
Answer:
x=3
Step-by-step explanation:
12/8=x/2
12×2=8x
24=8x
x=24/8
x=3
If a fence cost $18 for every 3 feet if it cost 30$ how much fencing will I get
The amount of fencing you will get is 5 feet.
What is division?Math operations include division as one of its types. This technique involves splitting the phrases or numbers into the same amount of components.
If $18 is the cost for every 3 feet of fencing, then as per the division operation the cost per 1 foot of fencing is,
$18/3 = $6.
So, if it costs $30, then the amount of fencing you will get is $30/$6 = 5 feet.
Therefore, the required amount of fencing is 5 feet.
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Please Hurry! 60 POINTS!!! Will give brainiest!
What is the average rate of change of the function over the interval x = 0 to x = 8?
Answer:
[tex]\frac{13}{145}[/tex]
An earthquake with a rating of 7.8 is
known to be a great earthquake that can
cause damage that extends several
hundred kilometers.
The value of x when the Richter scale rating is 7.9, rounded to the nearest whole number, is approximately 79,432,823.
The formula relating the Richter scale rating (r) and the intensity ratio (x) is r = log(x). To find the value of x when r is 7.9, we can rearrange the formula and solve for x,
x = 10ʳ
Substituting r=7.9 into the formula, we get,
[tex]x = log((10)^{7.9} )[/tex]
Using a calculator, we get,
x ≈ 79432823.09
Rounding this to the nearest whole number, we get,
x ≈ 79432823
Therefore, the value of x when the Richter scale rating is 7.9, rounded to the nearest whole number, is approximately 79,432,823.
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Complete question - What is the value of x when the Richter scale rating is 7.9 round your answer to the nearest
r=log x
r=rating of the earthquakes size on the Richter scale
x=ratio of earthquake intensity to a minimum level of intensity
Which shape has two pairs of parallel sides? (2 points)
a quadrilateral with one small square in each of the four corners, and single arrows going in the same direction for one pair of the opposite sides and double arrows for the other pair of opposite sides
a quadrilateral with single arrows going in the same direction for one pair of the opposite sides
a quadrilateral with double arrows going in the same direction for one pair of the opposite sides
a quadrilateral with sides of different lengths in the shape of an arrow
A quadrilateral with double arrows going in the same direction for one pair of the opposite sides is a Parallelogram, and it is the shape that has two pairs of parallel sides.
The shape that has two pairs of parallel sides is the third option: a quadrilateral with double arrows going in the same direction for one pair of the opposite sides.
This shape is called a parallelogram, which is a type of quadrilateral where opposite sides are parallel and congruent. In a parallelogram, each pair of opposite sides has the same length and the same arrow direction, which is what is represented by the double arrows in the description.
The other options do not fit the definition of a parallelogram. The first option describes a shape with four right angles, but only two pairs of parallel sides, which would make it a trapezoid. The second option describes a shape with only one pair of parallel sides, which is not enough to be a parallelogram. The fourth option describes a shape with sides of different lengths and in the shape of an arrow, which does not fit the definition of a parallelogram.
Parallelograms have many interesting properties, such as opposite angles being congruent and diagonals bisecting each other. They are also the basis for other geometric shapes, such as rectangles and rhombuses, which have additional properties due to their specific angles and side lengths.
A quadrilateral with double arrows going in the same direction for one pair of the opposite sides is a parallelogram, and it is the shape that has two pairs of parallel sides.
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. Tommy has started in a total of 109 RHS games, all football and baseball. The number of baseball games he started was five less than twice the number of football games he started. How many football games did Tommy start?
Answer:
Let's denote the number of football games Tommy started as "f" and the number of baseball games he started as "b."
We're given two pieces of information:
Tommy has started a total of 109 RHS games:
f + b = 109 (Equation 1)
The number of baseball games he started was five less than twice the number of football games he started:
b = 2f - 5 (Equation 2)
We can solve this system of equations to find the value of "f," which represents the number of football games Tommy started.
Substitute Equation 2 into Equation 1:
f + (2f - 5) = 109
Combine like terms:
3f - 5 = 109
Add 5 to both sides:
3f = 114
Divide both sides by 3:
f = 38
Therefore, Tommy started 38 football games.
Step-by-step explanation:
Answer:
Step-by-step explanation:
Tommy started with 71
. Two popcorn boxes are shown below. The boxes
have congruent openings and equal heights. If
the larger box of popcorn sells for $3.00, what
is a fair price for the smaller box?
The fair price for the smaller box should be $1.00.
How do we calculate?From the question, we have that the larger box of popcorn sells for $3.00 and the two boxes have congruent openings and equal heights, we then can make the assumption that the only difference between them is their volume.
The volume of a pyramid is found using the formula:
V = (1/3) B* h,
where 'B'= base area
'h' = height of the pyramid
In conclusion, we can say that The fair price for the smaller box should be $1.00 because a pyramid is 1/3 the volume of a prism.
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The complete question is attached
What is the mean of the distribution below?
CODE: Enter the mean as your code. Do NOT round your answer. Enter all
decimal places. Put the decimal in the correct spot as well
,10
X
X
X
X
X
Movie Theme
Weights of Dogs
X
X X X X
15
X
X
X
25
Weight in pounds
X
X
30
The mean of the distribution in this problem is given as follows:
19.5625 pounds.
How to calculate the mean of a data-set?The mean of a data-set is given by the sum of all observations in the data-set divided by the cardinality of the data-set, which represents the number of observations in the data-set.
The dot plot shows the absolute frequency of each observation in the context of the problem.
Considering the dot plot, the sum of the observations in this problem is given as follows:
2 x 12 + 4 x 15 + 1 x 16 + 1 x 18 + 2 x 20 + 1 x 22 + 3 x 25 + 2 x 29 = 313.
The number of observations is given as follows:
2 + 4 + 1 + 1 + 2 + 1 + 3 + 2 = 16.
Hence the mean is given as follows:
313/16 = 19.5625 pounds.
Missing InformationThe problem is given by the image presented at the end of the answer.
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how do you plot ratios and rates as ordered pairs on the coordinate plane.?
Answer: To plot ratios and rates as ordered pairs on the coordinate plane, you can follow these steps:
Understand the ratio or rate: Make sure you understand the meaning and value of the ratio or rate you are working with. A ratio compares two quantities, while a rate compares two quantities with different units.
Choose a coordinate system: Set up a coordinate system on the plane with an x-axis and a y-axis. Determine the range of values you want to plot on each axis based on the given ratio or rate.
Determine the values for the axes: Assign the x-axis and y-axis values based on the given ratio or rate. For ratios, you can assign the values of the ratio to the x and y axes directly. For rates, you will need to convert the rate into a ratio by choosing a unit for one of the quantities.
Plot the points: Use the values obtained from step 3 as the x and y coordinates for each ordered pair. Plot the points on the coordinate plane.
Connect the points (if applicable): If you have multiple points, you can connect them with a line to show the relationship between the ratios or rates.
Label the axes and title the graph (if applicable): Add labels to the x and y axes to indicate the quantities being compared. You can also add a title to the graph to describe the relationship being represented.
Step-by-step explanation:
452.25 ÷ 10.5 what is the answer to this please tell me
Answer:
43.07
Step-by-step explanation:
remove the decimals and divide them as whole numbers then after the successful division return the decimal places according to the number of decimal places in each that is minus the number of decimal places in the divisor from the numbers of decimal places in the dividend
given that f(x) = x^2 - 1
find f(5)
Answer:
24
Step-by-step explanation:
As x is now equal to 5, all you have to do is substitute it into were x is in the f(x) formula given.
x^2-1 turns into (5)^2-1=
25-1=
24